Mathematical Sciences: Coherent and Chaotic Phenomena in PDE's

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The mathematics involved in these studies covers a broad spectrum from the theory of integrable and almost integrable systems and rigorous analysis in pde's to the more intuitive ideas best understood in a geometrical setting. In many cases, and specifically in the investigations in convective patterns and optics, real experiments are used as a guide to develop and check the validity of models. In all cases, each theoretical investigation is accompanied by extensive numerical experiments. An interactive environment (which is significantly enhanced by many scientific visitors) makes Arizona an excellent place for the training of students. Indeed, graduate students are heavily involved in the research described in this proposal.